Question

A mall has six different bakeries, namely Bakery A,B,C,D,E,F . Assume each customer that visits the...

A mall has six different bakeries, namely Bakery A,B,C,D,E,F . Assume each customer that visits the mall is equally likely to choose any of the six different bakeries, independent of the choices of the previous customers.

  1. The number of customers going to the mall during the first 10 minutes of business at the start of the day is a Poisson random variable with mean 8. Compute the expected value of the number of bakeries that will serve customers during the first 10 minutes.

It is now lunchtime! Assume that a group of 18 people from a nearby factory is craving for breads and cakes from the local bakeries so they arrive at the mall together. Continue to make the assumptions stated above: that each person selects a bakery uniformly at random from the 6 choices, independently of the choices of the other people.

  1. What is the probability that each bakery gets the same number of customers from this group of 18 workers?
  2. Let A be the number of these 18 people who go to Bakery A, and let B be the number of people who go to Bakery B. Write a formula for the joint probability mass function p(a,b) of the random variables A and B.

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